Calculus Volume 3 · free preview
Cylindrical and Spherical Coordinates
Cylindrical coordinates adapt polar coordinates to space with a height, and spherical coordinates use radial distance and two angles, each system simplifying triple integrals over symmetric regions.
1. Cylindrical coordinates
Cylindrical coordinates
2. Spherical coordinates
Spherical coordinates
3. Choosing the system
Choosing the system
4. The Jacobian preview
The Jacobian preview
5. Cylindrical definition
Cylindrical coordinates are which combination?
6. Spherical phi meaning
In spherical coordinates, the angle phi measures what?
7. Volume element Jacobian
The spherical volume element is which expression?
8. Conversion example
The point (1, 1, 0) in Cartesian has cylindrical coordinates which triple?
9. When spherical wins
A triple integral over a solid ball is simplest in which coordinate system?
10. Cylinder surface constant
In cylindrical coordinates, the surface r = 2 is which solid's boundary? Answer with one word.
11. Rho constant surface
In spherical coordinates, the surface rho = 3 is a sphere. As a single word, what surface? Answer with one word.
12. Phi constant surface
The surface phi = pi/4 is a cone about the z axis. As a single word, what surface? Answer with one word.
13. Theta range uniqueness
The spherical and cylindrical systems share the azimuthal angle theta. Over what range does a full turn run? Answer like 0 to 2 pi.
14. Z conversion cylindrical
Cylindrical coordinates leave which coordinate unchanged from Cartesian? Answer with one lowercase letter.
Practice this interactively
Free account · instant grading · spaced review that schedules itself.
Start this course for free